instructor: vincent duffy, ph.d. associate professor of ie lab 2 tutorial – uncertainty in...

Instructor: Vincent Duffy, Ph.D.Instructor: Vincent Duffy, Ph.D.

Associate Professor of IE Associate Professor of IE

Lab 2 Tutorial – Uncertainty in Decision MakingLab 2 Tutorial – Uncertainty in Decision Making

Fri. Feb. 2, 2006Fri. Feb. 2, 2006

IE 486 Work Analysis & Design IIIE 486 Work Analysis & Design II

Today – IE 486 Lab 2 tutorialToday – IE 486 Lab 2 tutorial

Discussion on uncertainty in decision making – Discussion on uncertainty in decision making – related to economic decision making and related to economic decision making and material from ch.7 in Wickens on Decision material from ch.7 in Wickens on Decision making in the context of human factors and making in the context of human factors and ergonomics.ergonomics.

In lab exercise: In lab exercise: Suppose the range of outcomes is known, but Suppose the range of outcomes is known, but the probability distribution is the probability distribution is unknownunknown (uncertain). Use a sheet of (uncertain). Use a sheet of paper to illustrate the selection of alternative A, B or C based on paper to illustrate the selection of alternative A, B or C based on four different analytical criteria known as Maxi-min, Maxi-max, Mini-four different analytical criteria known as Maxi-min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on your max regret, and equal likelihood. Write the payoff matrix on your sheet of paper and re-calculate to decide based on each of the four sheet of paper and re-calculate to decide based on each of the four criteria.criteria.

Lab 2 Exercise: Decision Making & Uncertainty. Lab 2 Exercise: Decision Making & Uncertainty. Suppose the range of outcomes is known, but the probability distribution is Suppose the range of outcomes is known, but the probability distribution is

unknownunknown (uncertain). Use a sheet of paper to illustrate the selection of (uncertain). Use a sheet of paper to illustrate the selection of alternative A, B or C based on four different analytical criteria known as Maxi-alternative A, B or C based on four different analytical criteria known as Maxi-

min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on your sheet of paper and re-calculate to decide based on each of the four criteria.your sheet of paper and re-calculate to decide based on each of the four criteria.

Observed outcomes of four trials are shown in the payoff matrix below. Observed outcomes of four trials are shown in the payoff matrix below. For each method, determine the expected outcomes before making your For each method, determine the expected outcomes before making your decision. decision. What is illustrated by the use of the different analytical techniques?What is illustrated by the use of the different analytical techniques?

observed outcome observed outcome expectedexpectedalternativealternative______11______22______33______4____ outcome4____ outcome ______ ______ A 6 0 1 3 A 6 0 1 3 B 2 4 4 1B 2 4 4 1 C 0 1 3 8 C 0 1 3 8

1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic viewtry to maximize the minimum outcometry to maximize the minimum outcomea. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome. possible outcome.b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).

2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic viewtry to maximize the maximum outcometry to maximize the maximum outcomea. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the bestbest possible outcome. possible outcome.b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).

3. 3. MiniMini--maxmax regretregret criteria criteria – Mini-max Regret: minimize the maximum possible regret.Mini-max Regret: minimize the maximum possible regret.– regret: difference between regret: difference between observedobserved and and bestbest payoff. payoff. 4. 4. EqualEqual--likelihoodlikelihood criteria criteria

a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.b. maximize the b. maximize the expectedexpected value. value.

from Chapter 4 in Babcock in Managing Engineering and from Chapter 4 in Babcock in Managing Engineering and Technology (Babcock, 1991).Technology (Babcock, 1991).– especially...especially...

Decision making under uncertainty. p. 74-75 (today) Decision making under uncertainty. p. 74-75 (today) – In Babcock, D.L. 1991. Managing engineering and technology: an In Babcock, D.L. 1991. Managing engineering and technology: an

introduction to management for engineers, Prentice-Hall: Englewood introduction to management for engineers, Prentice-Hall: Englewood Cliffs, NJ.Cliffs, NJ.

You may consider ‘economic’ decision making (related to You may consider ‘economic’ decision making (related to decisions made on investment alternatives) somewhat decisions made on investment alternatives) somewhat different from ‘cognitive’ considerations in decision making different from ‘cognitive’ considerations in decision making (related to decisions made during a task) from the Wickens (related to decisions made during a task) from the Wickens text. text.

However, this material may be considered to help bridge the However, this material may be considered to help bridge the material without considering ‘time value of money’ yet.material without considering ‘time value of money’ yet.

Analytical tools for decision making Analytical tools for decision making under uncertaintyunder uncertainty

Uncertainty - example 1 Uncertainty - example 1

In a discussion of forecasting, and decision making In a discussion of forecasting, and decision making – Suppose the range of outcomes is known, but the Suppose the range of outcomes is known, but the

probability distribution is probability distribution is unknownunknown (uncertain). (uncertain).

1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic view– try to maximize the minimum outcometry to maximize the minimum outcome– a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible possible

outcome.outcome.– b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).


In a discussion of forecasting, and decision making In a discussion of forecasting, and decision making

Suppose the range of outcomes is known, but the probability distribution is Suppose the range of outcomes is known, but the probability distribution is unknownunknown (uncertain). (uncertain).

1. 1. MaxiMaxi--minmin criteria - pessimistic view criteria - pessimistic viewtry to maximize the minimum outcometry to maximize the minimum outcome

a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome. possible outcome.

b. choose the best (of those previously chosen).b. choose the best (of those previously chosen).

Example 1) Suppose we have the following payoff matrix Example 1) Suppose we have the following payoff matrix

observed outcome expectedobserved outcome expected

alternativealternative______11______22______33______4____ outcome4____ outcome ______ ______

A 6 0 1 3 A 6 0 1 3

BB 2 4 4 1 2 4 4 1

C 0 1 3 8 C 0 1 3 8


In a discussion of forecasting, and decision making In a discussion of forecasting, and decision making

Suppose the range of outcomes is known, but the probability distribution is Suppose the range of outcomes is known, but the probability distribution is unknownunknown (uncertain). (uncertain).


a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome. possible outcome.





A 6 0 1 3 0A 6 0 1 3 0

BB 2 4 4 1 2 4 4 1

C 0 1 3 8 C 0 1 3 8



a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible outcome.possible outcome.





A 6 0 1 3 0A 6 0 1 3 0

BB 2 4 4 1 2 4 4 1 1 1

C 0 1 3 8 C 0 1 3 8



a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the worstworst possible possible outcome.outcome.





A 6 0 1 3 0A 6 0 1 3 0

BB 2 4 4 1 2 4 4 1 1 1

C 0 1 3 8 0C 0 1 3 8 0

for maxi-min criteria: choose Bfor maxi-min criteria: choose B


2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic view

try to maximize the maximum outcometry to maximize the maximum outcome

a. for any given alternative (eg. A,B, or C), assume a. for any given alternative (eg. A,B, or C), assume the the bestbest possible outcome. possible outcome.



2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic viewtry to maximize the maximum outcometry to maximize the maximum outcome

a. for any given alternative (eg. A,B, or C), assume the a. for any given alternative (eg. A,B, or C), assume the bestbest possible outcome. possible outcome.





A 6 0 1 3 A 6 0 1 3

BB 2 4 4 1 2 4 4 1

C 0 1 3 8 C 0 1 3 8


2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic viewtry to maximize the maximum outcometry to maximize the maximum outcome






A 6 0 1 3 6A 6 0 1 3 6

BB 2 4 4 12 4 4 1

C 0 1 3 8 C 0 1 3 8

Uncertainty - example 2 Uncertainty - example 2 2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic view







A 6 0 1 3 6A 6 0 1 3 6

BB 2 4 4 1 2 4 4 1 4 4

C 0 1 3 8 C 0 1 3 8

Uncertainty - example 2 Uncertainty - example 2 2. 2. MaxiMaxi--maxmax criteria - optimistic view criteria - optimistic view







A 6 0 1 3 6A 6 0 1 3 6

BB 2 4 4 1 2 4 4 1 4 4

C 0 1 3 8 8C 0 1 3 8 8

for maxi-max criteria: choose Cfor maxi-max criteria: choose C

Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria – Mini-max Regret: minimize the maximum possible Mini-max Regret: minimize the maximum possible

regret.regret.– regret: difference between regret: difference between observedobserved and and bestbest payoff. payoff.

eg. suppose we chose eg. suppose we chose BB, but in outcome 1, if we had , but in outcome 1, if we had chosen chosen AA we could have had we could have had 66 (from (from AA) instead of ) instead of 22 (from (from BB). ).

So we have So we have regretregret…if only we had chosen …if only we had chosen AA, we could , we could

have had have had 44 more! more!

Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria

Mini-max Regret: minimize the maximum possible regret.Mini-max Regret: minimize the maximum possible regret.

regret: difference between regret: difference between observedobserved and and bestbest payoff. payoff.

Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcomeobserved outcome (regret matrix) observed outcome

alternativealternative______11______22______33______4____ _______ _1 2 3 44____ _______ _1 2 3 4______maxmax______

A 6 0 1 3 A A 6 0 1 3 A

BB 2 4 4 1 2 4 4 1 B B

C 0 1 3 8 C C 0 1 3 8 C

for mini-max regret criteria: *choose Afor mini-max regret criteria: *choose A


eg. suppose we chose eg. suppose we chose BB, but in outcome 1, if we had chosen , but in outcome 1, if we had chosen AA we could have had we could have had 66 (from (from AA) instead of ) instead of 22 (from (from BB). So we ). So we have have regretregret…if only we had chosen …if only we had chosen AA, we could have had , we could have had 44 more! more!


alternativealternative______11______22______33______4____ ______ _ _1 2 3 44____ ______ _ _1 2 3 4______maxmax______

A 6 0 1 3 A 0 A 6 0 1 3 A 0

BB 2 4 4 1 2 4 4 1 B 4 B 4

C 0 1 3 8 C 6 C 0 1 3 8 C 6



alternativealternative______11______22______33______4__________ _ _1 2 3 44__________ _ _1 2 3 4______maxmax______

A 6 0 1 3 A 0 4 A 6 0 1 3 A 0 4

BB 2 4 4 1 2 4 4 1 B 4 0 B 4 0

C 0 1 3 8 C 6 3 C 0 1 3 8 C 6 3



alternativealternative______11______22______33______4____ __________ _1 2 3 44____ __________ _1 2 3 4______maxmax______

A 6 0 1 3 A 0 4 3 A 6 0 1 3 A 0 4 3

BB 2 4 4 1 2 4 4 1 B 4 0 0 B 4 0 0

C 0 1 3 8 C 6 3 1 C 0 1 3 8 C 6 3 1

Uncertainty - example 3Uncertainty - example 33. 3. MiniMini--maxmax regretregret criteria criteria Example 3) Suppose we have a payoff matrix (payoff) Example 3) Suppose we have a payoff matrix (payoff)

observed outcome (regret matrix) observed outcomeobserved outcome (regret matrix) observed outcome

alternativealternative______11______22______33______4____ __________ __1 2 3 44____ __________ __1 2 3 4______maxmax______

A 6 0 1 3 A 0 4 3 5 5 A 6 0 1 3 A 0 4 3 5 5

BB 2 4 4 1 2 4 4 1 B 4 0 0 7 7 B 4 0 0 7 7 C 0 1 3 8 C 6 3 1 0 C 0 1 3 8 C 6 3 1 0

66

for mini-max regret criteria: choose Afor mini-max regret criteria: choose A

Uncertainty - example 4Uncertainty - example 44. 4. EqualEqual--likelihoodlikelihood criteria criteria – this looks more like a ‘risk’ problem because you this looks more like a ‘risk’ problem because you

do use ‘assumed’ probabilitiesdo use ‘assumed’ probabilities

a. for any given alternative (eg. A,B, or C), a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.assume all outcomes are equally likely.

b. maximize the b. maximize the expectedexpected value. value.

Uncertainty - example 4Uncertainty - example 44. 4. EqualEqual--likelihoodlikelihood criteria criteria

a. for any given alternative (eg. A,B, or C), assume all a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.outcomes are equally likely.

b. maximize the b. maximize the expectedexpected value. value.




A 6 0 1 3 (6+0+1+3)/4 = 10/4A 6 0 1 3 (6+0+1+3)/4 = 10/4

BB 2 4 4 1 2 4 4 1

C 0 1 3 8 C 0 1 3 8

Uncertainty - example 4Uncertainty - example 44. 4. EqualEqual--likelihoodlikelihood criteria criteria Example 4) Suppose we have the following payoff matrix Example 4) Suppose we have the following payoff matrix



A 6 0 1 3 (6+0+1+3)/4 = 10/4A 6 0 1 3 (6+0+1+3)/4 = 10/4

BB 2 4 4 1 2 4 4 1 (2+4+4+1)/4 = 11/4 (2+4+4+1)/4 = 11/4

C 0 1 3 8 (0+1+3+8)/4 = 12/4C 0 1 3 8 (0+1+3+8)/4 = 12/4

for maxi-max criteria: choose Cfor maxi-max criteria: choose C

instructor: vincent duffy, ph.d. associate professor of ie lab 2 tutorial – uncertainty in...

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